One refined passport of genus 14 with automorphism group $C_{58}$

• Label: 14.58-2.0.2-29-58.20
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(C_{58}\)
• Signature: \([ 0; 2, 29, 58 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$C_{58}$
Group identifier:	$[58,2]$
Signature:	$[ 0; 2, 29, 58 ]$

Conjugacy classes for this refined passport:

$2, 22, 35$

Jacobian variety group algebra decomposition:

$A_{14}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,30) (2,31) (3,32) (4,33) (5,34) (6,35) (7,36) (8,37) (9,38) (10,39) (11,40) (12,41) (13,42) (14,43) (15,44) (16,45) (17,46) (18,47) (19,48) (20,49) (21,50) (22,51) (23,52) (24,53) (25,54) (26,55) (27,56) (28,57) (29,58)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x^{29}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.58-2.0.2-29-58.20.1

	(1,30) (2,31) (3,32) (4,33) (5,34) (6,35) (7,36) (8,37) (9,38) (10,39) (11,40) (12,41) (13,42) (14,43) (15,44) (16,45) (17,46) (18,47) (19,48) (20,49) (21,50) (22,51) (23,52) (24,53) (25,54) (26,55) (27,56) (28,57) (29,58)
	(1,21,12,3,23,14,5,25,16,7,27,18,9,29,20,11,2,22,13,4,24,15,6,26,17,8,28,19,10) (30,50,41,32,52,43,34,54,45,36,56,47,38,58,49,40,31,51,42,33,53,44,35,55,46,37,57,48,39)
	(1,39,19,57,8,46,26,35,15,53,4,42,22,31,11,49,29,38,18,56,7,45,25,34,14,52,3,41,21,30,10,48,28,37,17,55,6,44,24,33,13,51,2,40,20,58,9,47,27,36,16,54,5,43,23,32,12,50)